Colored Measurement Noise Research Articles

Dual Foot-Mounted Localisation Scheme Employing a Minimum-Distance-Constraint Kalman Filter under Coloured Measurement Noise

Dual Foot-Mounted Localisation Scheme Employing a Minimum-Distance-Constraint Kalman Filter under Coloured Measurement Noise

Dual Kalman Filter Based on a Single Direction under Colored Measurement Noise for INS-Based Integrated Human Localization

For inertial-based integrated pedestrian navigation, the navigation environment might affect the positioning accuracy in different directions. Meanwhile, complex filtering algorithms can reduce computational efficiency. Therefore, one dual Kalman filter (KF) based on a single direction under a colored measurement noise (CMN) scheme is developed herein to improve the robustness and operational efficiency. The proposed method involves designing a data fusion model for the KF that integrates data from an inertial navigation system (INS) and ultrawideband (UWB). Subsequently, the INS/UWB integrated model-based KF under CMN (cKF) will be derived. Then, two sub-cKFs are proposed to fuse the data in the east and north directions, respectively. The empirical findings highlight the superior performance of the proposed approach over the KF for position estimation accuracy and runtime reduction, demonstrating its effectiveness.

Improved UFIR Filter for Fusing Recent INS-assisted Visual Measurement under Colored Measurement Noise in UAV Landing

Improved UFIR Filter for Fusing Recent INS-assisted Visual Measurement under Colored Measurement Noise in UAV Landing

Robust sequential fusion Kalman estimators with asymptotic equivalence and stability for networked uncertain sensor systems

For networked uncertain sensor systems (NUSSs) with an improved unified sensor model with “hard” and “soft” sensors including five uncertainties plus two-step random measurement delays and colored measurement noises, applying the block matrix inversion formula, a new sequential inverse covariance fusion (SICF) approach is presented. It can sequentially compute the global inverse covariance according to the time order of the received data, but need not wait until all data are received. The corresponding minimax robust time-varying and steady-state sequential fusion (SF) Kalman estimators (predictor, filter, and smoother) are presented in the sense that their actual error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. They have lower computation complexities and higher accuracies equivalent to ones of the robust optimal batch-fusion (BF) Kalman estimators, and are suitable for real-time applications. Their asymptotic equivalence, absolute asymptotic stability, and accuracy relations are proved. Their strict complexity analysis is given. They constitute a novel universal robust SF estimation, convergence and stability theory for NUSSs. One simulation example applied to the uncertain ARMA signal processing verifies the effectiveness of the proposed approach and theory.

Estimation of wiener nonlinear systems with measurement noises utilizing correlation analysis and Kalman filter

AbstractThis paper is concerned with parameter estimation of Wiener systems with measurement noises employing correlation analysis method and adaptive Kalman filter. The presented Wiener system consists of two series blocks, that is, a dynamic block represented by auto‐regressive moving average (ARMA) model, and static nonlinear block established by neural fuzzy model. Aim at estimating separately the two blocks, the separable signals are introduced. First, applying the separable signals to decouple the identification of linear dynamic block from that of static nonlinear block, then ARMA model parameters are estimated employing correlation function‐based least squares principle. Moreover, aiming at handle with error caused by colored measurement noise, adaptive Kalman filter technique and cluster method are introduced to estimate parameter of the nonlinear block and noises model, enhancing parameter estimation precision. The accuracy and applicability of estimated scheme presented are verified through numerical simulation and nonlinear process, the results demonstrate that it is feasible for estimating the Wiener systems in the presence of colored measurement noises.

Robust Kalman Filter for Systems With Colored Heavy-Tailed Process and Measurement Noises

In this paper, we consider the robust state estimation for a linear system with colored heavy-tailed process and measurement noises. We employ the state augmentation and measurement differencing methods to whiten the colored noise and use the Student’s t distribution to model the heavy-tailed property, which makes a new state space model with the augmented state vector. The posterior estimation of the system state, inaccurate scale matrices, and auxiliary parameters are jointly inferred with the variational Bayes method by constructing the hierarchical Gaussian forms of the prediction and likelihood probability density functions and selecting the proper prior distributions of the scale matrices and auxiliary parameters. A typical target tracking simulation is given to confirm the performance of the proposed robust Kalman filter.

Extended Kalman/UFIR Filters for UWB-Based Indoor Robot Localization Under Time-Varying Colored Measurement Noise

In indoor robot localization by using Ultra-Wide Band (UWB), the extended Kalman filter (EKF)-based algorithms suffer from the Colored Measurement Noise (CMN) that degrades the localization accuracy and causes the divergence. To overcome this issue, we develop a hybrid colored EKF and colored extended unbiased Finite Impulse Response (EFIR) filter (cEKF/EFIR filter) employing measurement differences. We also develop this algorithm using a filter bank on merged averaging horizons to be adaptive to time-varying CMN and call it the aEKF/EFIR filter. Experimental testing is provided in UWB-based indoor mobile robot localization environments. It is shown that the end-to-end cEKF/EFIR and aEKF/EFIR filtering algorithms have better performances than the EKF, EFIR filter, and their modifications for CMN.

TFNet: Few-shot identification of LTI systems based on convolutional neural networks

Recent research in system identification aims to reduce the amount of data required for identification and the persistence of excitation while maintaining the identified model’s generalization and goodness of fit. This paper introduces TFNet11TF stands for Transfer Function. as a few-shot transfer function identification method for industrial systems. TFNet enables both structural and parametric identification of industrial linear time-invariant systems from their pulse response. Furthermore, TFNet identifies properties such as the existence of integrator and non-minimum-phase zeros in systems, as long as the order of the system is two or smaller. We compare the performance of TFNet with that of classical and state-of-the-art rival methods on syntactic data, where TFNet outperforms other methods by a wide margin. Furthermore, experiments on two laboratory setups: an air temperature control system and a two-tank control system demonstrate that TFNet estimates a close model to the ground truth despite colored measurement noise in the first experiment, and without driving the system out of its operating point in the latter case.22The python implementation of TFNet is in https://github.com/abbasnosrat/TFNet.git.

Sequential fusion estimation for multisensor multirate systems with measurement outliers

AbstractThis paper investigates the suboptimal sequential fusion estimation problem for multisensor multirate networked systems with colored measurement noises under the interference of measurement outliers. The saturation function is used to constrain the innovation polluted by measurement outliers. Due to diverse physical restrictions, the sampling period of the sensor is assumed to be different from the update period of the system state, thereby better reflecting the engineering practice. The lifting technique is used to convert the multirate sampling system into a single‐rate form. By solving the matrix difference equation, an upper bound of the filtering error covariance is obtained, and the filter gain is then derived, which can minimize the upper bound of the error covariance. Finally, a simulation example is given to demonstrate the effectiveness of the proposed sequential fusion method for multirate sampling systems under outlier interference.

Dynamic displacement estimation and modal analysis of long-span bridges integrating multi-GNSS and acceleration measurements

Compared with acceleration-based modal analysis, displacement can provide a more reliable and robust identification result for output-only modal analysis of long-span bridges. However, the estimated displacements from acceleration records are frequently unavailable due to unrealistic drifts. Aiming at obtaining more accurate and stable results for determining the modal parameters, this study develops a multi-rate weighted data fusion approach for estimating displacement responses in dynamic monitoring of structures based on global navigation satellite system (GNSS) and acceleration measurements. The approach initially derives the local estimations from displacement and acceleration sensors via a Kalman filter algorithm with colored measurement noise, and later uses a weighted fusion criterion of scalar linear minimum variance to fuse the results of local estimations. Then, structural modal pamameters are identified by employing data-driven stochastic subspace identification (SSI) algorithm. The proposed approach is validated in a four degree-of-freedom numerical model and then applied to a long-span bridge in engineering practice. The results illustrate that the proposed approach can reduce the error of GNSS-obtained displacement and expand recognizable frequency range by introducing dynamic displacement component from acceleration measurement.

TWOR: Improving Modeling and Self-Localization in RFID-Tag Networks Under Colored Noise

This paper discusses the three-wheeled omnidirectional robot (TWOR) self-localization in radio frequency identification (RFID) tag environments. The nonlinear TWOR model is significantly improved by using geometric interpretation and incremental time representation in discrete time. The TWOR position and heading are self-estimated using distance measurements to RFID tags and a digital gyroscope in the presence of typical colored measurement noise (CMN). The extended unbiased finite impulse response (EFIR) is developed along with the extended Kalman filter (EKF) and their versions, cEKF and cEFIR, modified for Gauss-Markov CMN. A particle filter is used as a benchmark. It is shown that the cEFIR filter is more robust than the cEKF and almost as robust as the particle filter, although the latter is less accurate in real time.

Stochastic Event-Triggered Fault Detection and Isolation Based on Kalman Filter.

In this article, the robust fault detection and isolation (FDI) Kalman filter is extended based on stochastic event-triggered schedulers for discrete linear systems consisting of deterministic/stochastic unknown inputs with nonzero mean and colored measurement noise. In the proposed FDI method, first, a subspace of the main system that significantly attenuates disturbance effects is proposed. After that, the fusion method is proposed for dealing with the colored measurement-noise problem in designing the Kalman filter and preventing from leading to measurement noise with zero mean and zero covariance. The stochastic event-triggered schedulers are considered as Gaussian functions. Therefore, the Gaussian property of innovation sequence is preserved, and consequently, the recursive equation of the Kalman filter need not be extended based on approximation techniques. Finally, design parameters are chosen based on the convex optimization problem such that the lowest communication rate between the sensor node and FDI filter, and also the best FDI performance are achieved. The proposed FDI method is evaluated to detect and isolate stator interturn short circuit and broken rotor bars faults with unbalanced voltage as disturbance in three-phase induction motors.

Estimation of States Under Colored Measurement Noise (CMN) Using UFIR and Kalman Filters Modified

The estimate process of a moving target trajectory is a well-known problem, where the main objective is to improve the estimation of object position. During the tracking are presented errors or variations between the true position and the estimated. In this paper, we treat such variations as a Gauss-Markov colored measurement noise (CMN). The estimation process is performed in predict and update, where the prediction indicates the next position of the bounding box, and the update is a correction step, which includes the new measurement of the tracking model and helps to improve the estimation. Looking for this improvement we use Kalman and Unbiased Finite Impulse Response filters in the standard version and modified for CMN to demonstrate the filter with the best performance. To test the most robust filter we use a high coloredness factor. The tests were carried out with simulated data (ideal and no ideal conditions) and with benchmark data (no ideal conditions). The UFIR modified for the CMN algorithm showed favorable results with high precision and low RMSE in the object tracking process with benchmark data and under no ideal conditions. While KF CMN showed better results under ideal conditions.

Estimation of states with data under Colored Measurement Noise (CMN)

Object tracking is an area of study of great interest to various researchers, where the main objective is to improve estimation of the trajectory of a moving object. This is due to the fact that in the object tracking process there are usually variations between the true position of the moving object and the estimated position, that is, the object is not exactly followed throughout its trajectory. These variations can be thought of as Colored Measurement Noise (CMN) caused by the object and the movement of the camera frame. In this paper, we treat such differences as Gauss-Markov colored measurement noise.We use Finite Impulse Response and Kalman Filters with a recursive strategy on the tracking: predict and update. To demonstrate the filter with the best performance, tests were carried out with simulated trajectories and with benchmarks from a database available online. The UFIR modified for CMN algorithm showed favorable results with high precision and accuracy in the object tracking process with benchamark data and under no ideal conditions.While KF CMN showed better results in tests with simulated data under ideal conditions.

Poisson multi‐Bernoulli mixture filters with coloured measurement noise

To solve multitarget tracking (MTT) problems with coloured measurement noise, this study proposes a Poisson multi-Bernoulli mixture filter with coloured measurement noise (PMBM-CMN) and a robust PMBM-CMN filter. By using the measurement differencing method and state augmentation approach, the proposed PMBM-CMN filter transforms a state estimation problem with coloured measurement noise into a problem with white measurement noise. However, covariances of the true process and measurement noise in the proposed PMBM-CMN filter are time-varying and unknown, which may degrade the filtering performance. Therefore, a robust PMBM-CMN filter is proposed for estimating the augmented state, including the kinematic state, the predicted state covariance, and the white measurement noise covariance. For linear Gaussian systems, the augmented state is modelled as a Gaussian inverse Wishart inverse Wishart (GIWIW) distribution. The variational Bayesian method is also employed to guarantee the conjugacy of the GIWIW density. Simulation results demonstrate the ability of the PMBM-CMN filter to solve MTT problems with coloured measurement noise and show that the robust PMBM-CMN filter based on the GIWIW model (GIWIW-PMBM-CMN) has the best overall performance in comparison with existing state-of-the-art filters.

Distributed Kalman filter for UWB/INS integrated pedestrian localization under colored measurement noise

Colored Measurement Noise (CMN) has a great impact on the accuracy of human localization in indoor environments with Inertial Navigation System (INS) integrated with Ultra Wide Band (UWB). To mitigate its influence, a distributed Kalman Filter (dKF) is developed for Gauss–Markov CMN with switching Colouredness Factor Matrix (CFM). In the proposed scheme, a data fusion filter employs the difference between the INS- and UWB-based distance measurements. The main filter produces a final optimal estimate of the human position by fusing the estimates from local filters. The effect of CMN is overcome by using measurement differencing of noisy observations. The tests show that the proposed dKF developed for CMN with CFM can reduce the localization error compared to the original dKF, and thus effectively improve the localization accuracy.

Design of the modified fractional central difference Kalman filters under stochastic colored noises

For state estimation of discrete nonlinear fractional stochastic systems, this study presents two innovative modified fractional central difference Kalman filters. We consider a complicated scenario where the process noise or measurement noise in the system become colored noise. Firstly, the nonlinear function is linearized by utilizing the Stirling polynomial interpolation formula. Thus there is no need to calculate the Jacobi matrix for both algorithms, which means very few application limitations. Then, based on the augmented-state method, we develop an augmented state fractional central difference Kalman filter under the scenario of colored process noise. Afterwards, a state estimation algorithm for handling stochastic systems containing colored measurement noise is put forward by using the measurement expansion method. Finally, to perform the superiority of the developed algorithms, several simulations are carried out. As well, the algorithms derived in this paper are contrasted with the original fractional central difference Kalman filter and three other algorithms. Notably, a simulation with engineering significance for the state-of-charge estimation for lithium-ion batteries is also introduced, Aside from the commonly used numerical simulation. The results verify the superiority of the developed algorithms in sense of estimation accuracy and real-time performance.

Improving Gaussianity of EMG Envelope for Myoelectric Robot Arm Control

Several methods have been developed in biomedical signal processing to extract the envelope and features of electromyography (EMG) signals and predict human motion. Also, efforts were made to use this information to improve the interaction of a human body and artificial protheses. The main operations here are envelope acquiring, artifacts filtering, estimate smoothing, EMG value standardizing, feature classifying, and motion recognizing. In this paper, we employ EMG data to extract the envelope with a highest Gaussianity using the rectified signal, where we deal with the absolute EMG signals so that all values become positive. First, we remove artifacts from EMG data by using filters such as the Kalman filter (KF), H1 filter, unbiased finite impulse response (UFIR) filter, and the cKF, cH1 filter, and cUFIR filter modified for colored measurement noise. Next, we standardize the EMG envelope and improve the Gaussianity. Finally, we extract the EMG signal features to provide an accurate prediction.

Enhanced fault detection and exclusion based on Kalman filter with colored measurement noise and application to RTK

With the development of high-precision safety–critical applications using global navigation satellite systems (GNSS), fault detection and exclusion (FDE) is indispensable to guaranteeing the integrity of a GNSS positioning and navigation system. Many FDE algorithms have been developed based on the standard Kalman filter (KF), assuming that GNSS measurements come with Gaussian uncorrelated white noise. The existence of colored noise in GNSS measurements, which is typical for positioning with low-cost receivers and in challenging environments will, however, degrade the performance of KF-based FDE algorithms. We proposed an FDE scheme based on improved KF considering colored noise (CKF) as a first-order autoregressive model to improve the FDE performance. The performance of the proposed CKF-based FDE algorithm was evaluated with an application to real-time kinematic positioning using a low-cost receiver. A CKF-based fault detection test, a fault identification test, a minimum detectable bias (MDB), error distribution, and positioning results were examined. The results showed that the CKF-based FDE can obtain realistic statistical information to improve integrity monitoring reliability. The fault detection test achieved a 17.83% improvement in FDE performance and a reduction in the false alarm rate, from 23.33 to 5.50%, compared with KF-based FDE. The tests also indicated that the CKF-based FDE can detect multiple faults with zero-miss detection. The fault identification test had an average improvement of 32.14%, and a more realistic MDB was obtained. The results of this study contribute to making objective decisions for the integrity monitoring of practical, precise GNSS positioning.

Three-Wheeled Omnidirectional Robot Localization in RFID-Tag Environments using UFIR Filtering

This paper describes a way to improve the indoor navigation of mobile robots using radio frequency identification (RFID) technology. A net of RFID tags is deployed in the navigation space. A measurement system measures distances from the tags to the robot with in the presence of the firstorder Markov-Gauss colored measurement noise (CMN) and is combined with a digital gyroscope to measure the robot heading. To increase the localization accuracy, the Kalman filter (KF) and unbiased finite impulse response (UFIR) modified for CMN are used. It is shown that the navigation system developed is more accurate than the basic one employing the standard KF and UFIR filter